Yes, since this 100 adults demonstrate just under 5% of the adult American population, the trials are considered independent.
We have n=100 and p=0.15 here.
np=100*0.15=15 ≥ 10,
nq=100*(1-0.15))=85 ≥ 10
The normality assumption can be used to approximate the binomial distribution.
Option A) is the correct answer.
The probability of seeing a specific value of such a continuous probability distribution is 0 percent.
Determine the prerequisites since a distinct distribution of probabilities.
The probability sum must equal one. So every probability should be between 0 and 1.
Describe how to determine the median of a separate random variable. To calculate the men of such a stochastic process, divide the total each value by it's own probability and afterwards add the results.
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One important use of the regression line is to do which of the following?
A. To determine the strength of a linear association between two variables
B. To determine if a distribution is unimodal or multimodal
C. To make predictions about the values of y for a given x-value
D. Both A and B are correct
The regression line can be used to determine the strength of a linear association between two variables, as well as to make predictions about the values of y for a given x-value.
The regression line is a type of mathematical model used to describe the relationship between two variables, typically denoted as x and y. The regression line is a straight line that best fits the data points of the two variables. This line can be used to make predictions about the values of y for a given x-value.
The equation of the regression line is y = mx + b, where m is the slope of the line, and b is the y-intercept. The slope of the line, m, represents the strength of the linear relationship between the two variables. It is calculated by dividing the covariance of the two variables by the variance of the independent variable (x). The y-intercept, b, is the point where the regression line crosses the y-axis. It is calculated by taking the mean of y and subtracting the slope of the line multiplied by the mean of x.
The regression line can also be used to determine the strength of the linear association between two variables. This is determined by calculating the correlation coefficient, which is a measure of how closely two variables are associated. The correlation coefficient is calculated by taking the covariance of the two variables, divided by the product of the standard deviation of each variable. A correlation coefficient of close to 1 indicates a strong positive linear association, while a correlation coefficient of close to -1 indicates a strong negative linear association.
In conclusion, the regression line can be used to determine the strength of a linear association between two variables, as well as to make predictions about the values of y for a given x-value.
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A movie theater is offering a special summer pass. Passholders pay $8 per movie for the first 5 movies and watch additional movies for free, up to a maximum of 15 movies. The function C gives the total cost, in dollars, for a passholder to watch n movies
The function is given as 6 < x < 15
How to solve for the functionAssuming that Pass members pay $8 each movie for the first five films, the equation y = 8x will be used to express this. Also, it is stated that after five films, additional films are free up to fifteen films. Thus, y = 40 will be the function used to represent this.
X represents the total number of films, while Y represents the monetary cost.
the function would be:
y = 8x{0 < x < 5}
y = 8 x 5
y = 40 {6 < x < 15}
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Please help what the answer for these questions
Answer:
unit rate = $ 10 per km.
y = 10x
Step-by-step explanation:
Unit rate:
Cost of travelling 1 km is $ 10. So, unit rate is $10
Equation:
If 'x' km distance is travelled, then cost 'y',
y = x * unit rate
y = x * 10
y = 10x
what is the greatest common factor of this equation
The greatest common factor of 30y⁸ +10y⁴ is 10y⁴
What is greatest common factor?The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4. GCF is often used to find common denominators.
The common factors of 30 are: 1,2,3,5,6,10,15,30
The common factors of 10 are : 1,2,5,10
therefore the greatest common factor is 10
The greatest common factor between y⁴ and y⁸;is y⁴
Therefore the greatest common factor of 30y⁸ +10y⁴ is 10y⁴ i.e 10y⁴(3y⁴+1)
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Use synthetic division to determine if x +3 is a factor of the given polynomial
[tex]2x^3+7x^2+3[/tex]
Answer:
After performing synthetic division, as the last number in the bottom row is not zero, this indicates that (x + 3) is not a factor of the given polynomial.
Step-by-step explanation:
Given polynomial function:
[tex]2x^3+7x^2+3[/tex]
To determine is (x + 3) is a factor of the given polynomial by the method of synthetic division:
Place "-3" in the division box.Write the coefficients of the dividend in descending order.Note: As the x term is missing, place a zero in its place.
[tex]\begin{array}{c|cccc}-3 &2&7&0&3\\\cline{1-1}\end{array}[/tex]
Bring the leading coefficient straight down:
[tex]\begin{array}{c|cccc}-3 &2&7&0&3\\\cline{1-1}&\downarrow&&&\\\cline{2-5}&2&&&\end{array}[/tex]
Multiply the number you brought down with the number in the division box and put the result in the next column (under the 7):
[tex]\begin{array}{c|crrr}-3 &2&7&0&3\\\cline{1-1}&\downarrow&-6&&\\\cline{2-5}&2&&&\end{array}[/tex]
Add the two numbers together and put the result in the bottom row:
[tex]\begin{array}{c|crrr}-3 &2&7&0&3\\\cline{1-1}&\downarrow&-6&&\\\cline{2-5}&2&1&&\end{array}[/tex]
Repeat:
[tex]\begin{array}{c|crrr}-3 &2&7&0&3\\\cline{1-1}&\downarrow&-6&-3&9\\\cline{2-5}&2&1&-3&12\end{array}[/tex]
The bottom row (except the last number) gives the coefficients of the quotient. The degree of the quotient is one less than that of the dividend. The last number in the bottom row is the remainder.
Therefore, if we divide the polynomial by (x + 3) we get:
[tex]2x^2+x-3+\dfrac{12}{x+3}[/tex]
As the last number in the bottom row is not zero, this indicates that (x + 3) is not a factor of the given polynomial.
The correlation coefficient ranges from which two values? a. 0 and 1 b. −1 and +1 c. minus infinity and plus infinity d. 1 and 100
The correlation coefficient ranges from -1 to +1. (option b)
What is correlation?Correlation is a measure that is used in statistics to measure the relationship that exists between two variables. Correlation can either be positive, negative or zero.
Positive correlation exists when two variables move in the same direction. The correlation coefficient usually ranges from 0 to 1. Negative correlation exists when the two variables move in different direction. The correlation coefficient usually ranges from -1 to 0. Zero correlation is when there is no relationship between the variables.
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on a car trip, jane ate some pretzels. after spilling and losing half of the pretzels, she at 14. her sister then ate on more than half the remaining pretzels, after which there was 3
The number of pretzels in the beginning was 44 pretzels solving the equation.
What is an Equation?An equation is a mathematical statement containing two expressions on either sides which are connected with an equal to sign.
Either sides of an equation is called as left hand side and right hand side.
Let the total number of pretzels = x
Pretzels has been spilled and lost half of the pretzels.
Remaining pretzels = x - x/2
Jane ate 14 pretzels.
Remaining pretzels = x - x/2 - 14
Her sister then ate one more than half the remaining pretzels.
Remaining pretzels = x - x/2 - 14 - [1/2 (x - x/2 - 14) + 1]
Remaining pretzels is 3.
So we get an equation,
x - x/2 - 14 - [1/2 (x - x/2 - 14) + 1] = 3
Solve for x.
x - x/2 - 14 - (x/2 - x/4 - 7 + 1) = 3
x - x/2 - x/2 + x/4 - 14 + 7 - 1 = 3
x/4 - 7 - 1 = 3
x/4 - 8 = 3
x/4 = 11
x = 44
Hence the total number of pretzels was 44.
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Your question is incomplete. The complete question is as follows.
On a car trip, Jane ate some pretzels. After spilling and losing half of the pretzels, she ate 14. Her sister then ate one more than half the remaining pretzels, after which there was 3 pretzels.
How many pretzels was there?
Three blankets and a sheet cost me RM190. Two sheets and a blanket cost a total of RM100. Find the cost of one blanket and one sheet
Answer:
Step-by-step explanation:
x is one blanket
y in one sheet
3x+y=190
2y+x=100
y=190-3x
2y+x=100
replace the y in the second equation with the first one
2(190-3x)+x=100
380-6x+x=100
380-5x=100
-5x=100-380
-5x=-280
x= -280/-5
x=56
replace the x with 56 so you can find the y
2y+56=100
2y=100-56
2y=44
y=44/2
y=22
so one blanket is 56 and a sheet is 22
Tasty trunks treats sends a selection of snacks in the mail each month and he bought a three month subscription for a friend use the one time coupon and receive five dollars off total cost Andy paid $37 at all which equation can use to find the regular cost of them for each month
Find the distance and round decimals to the nearest tenth! Please help me
Answer:
5
Step-by-step explanation:
Hey you right their come help me with some math
Answer:
B and E
Step-by-step explanation:
Information we need to know:
Like terms - a set of number which variables are the same
In the question we can see that there are two numbers that have the variable y and two numbers that have the variable of 0 (meaning that they are regular numbers)
Hence our options would be B and E
Hope this helps, have a lovely day! :)
81. 3% complete
Question
A recipe requires 1. 5 kilograms of eggs. How much is this in pounds?
1.5 kilograms of eggs is equivalent to approximately 3.31 pounds. Both kilograms and pounds are weight measuring units.
To convert kilograms to pounds, we can use the conversion factor that 1 kilogram is equal to 2.20462 pounds.
So to convert 1.5 kilograms of eggs to pounds, we can multiply 1.5 by 2.20462:
1.5 kilograms x 2.20462 pounds/kilogram = 3.30693 pounds
Therefore, 1.5 kilograms of eggs is equivalent to approximately 3.31 pounds. Both kilograms and pounds are weight measuring units. Kilograms are the primary unit of measurement for weight in the International System of Units (SI), while pounds are the primary unit of measurement for weight in the United States and other countries that use the imperial system of units. A kilogram is roughly equivalent to 2.20462 pounds. Kilograms are often used for scientific or medical purposes, while pounds are more commonly used for everyday weight measurements, such as for people's body weight or for weighing food in recipes.
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Write the logarithmic expression as a single logarithm.
1/2(log₂x + log ₂y) - 5 log ₂(x+6)
Answer:
We can use the following logarithmic identities to simplify the expression:
log a + log b = log (ab)
log a - log b = log (a/b)
n log a = log (a^n)
Using these identities, we can simplify the expression as follows:
1/2(log₂x + log₂y) - 5 log₂(x+6)
= 1/2 log₂(xy) - log₂(x+6)^5 (using the first two identities)
= log₂[(xy)^(1/2)/(x+6)^5] (using the third identity to combine the logarithms)
Therefore, the simplified expression is:
log₂[(xy)^(1/2)/(x+6)^5]
Step-by-step explanation:
$925 at 2.3% for 2.4 years
The interest for the given principal , time and rate is $ 51.06 . The Amount after interest is $ 976.06.
What is Simple Interest ?Simple interest is the amount of borrowing-related interest that is calculated using only the original principal and a constant interest rate. Compounding, in which borrowers end up paying interest on principal and interest that increases over a few of payment periods, is not a part of it.
Simple Interest = [tex]\frac{P*R*T}{100}[/tex]
where, P = principal, R = Rate of interest, T = Time.
Now in the given question,
Principal = $925
Rate= 2.3 %
Time = 2.4 years
Then,
Simple Interest,
[tex]=\frac{P*R*T}{100} \\\\=\frac{925*2.3*2.4}{100} \\\\=$51.06[/tex]
Hence the interest is $ 51.06 .
Amount after interest = P + I = 925 + 51.06 = $ 976.06.
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I need help ASAP
what is the domain of y=-16x^2+1700
The domain of the equation y = -16x^2 + 1700 is the set of all real numbers.
Explanation:
To find the domain of the equation y = -16x^2 + 1700, we need to determine the set of all real numbers for which the equation is defined.
Since the equation is a quadratic equation, it is defined for all real values of x. There are no restrictions on the values of x that can be plugged into the equation.
Therefore, the domain of the equation y = -16x^2 + 1700 is the set of all the real numbers.
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I need some help please
Answer:
1 ≤ x ≤ 9
Step-by-step explanation:
When you create a dot plot, you do which of these operations? Select all that apply.
a. Add a vertical axis showing frequency of observations.
b. Connect adjacent dots to create a polygon.
c. Place a dot along a horizontal scale for each observation.
d. "Pile up" dots that are too close to show separately
When you create a dot plot, the operations that you have to do are:
c. Place a dot along a horizontal scale for each observation.
d. "Pile up" dots that are too close to show separately
A dot plot is a simple way of representing numerical data. It consists of a horizontal axis and a series of dots that are placed along it to represent the values of individual observations. Each dot corresponds to one observation, and its position along the axis represents its value.
Option (a) is not correct because a dot plot typically does not have a vertical axis showing frequency of observations. Option (b) is not correct because connecting adjacent dots to create a polygon is not a common practice in dot plots. Instead, each dot represents a single observation, and dots are placed along a horizontal scale to show their value. If multiple observations have the same value, they are "piled up" on top of each other to avoid overcrowding the plot.
Therefore, the correct options are (c) Place a dot along a horizontal scale for each observation and d. "Pile up" dots that are too close to show separately
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Use the following conditional:
If a number is odd, then it is an integer and a prime number.
Which is the hypothesis of the conditional?
A. A number is odd.
B. A number is a prime number.
C. A number is either an integer or a prime number.
D. A number is both an integer and a prime number.
The equation T=2π√L/32 models the relationship between the length of a pendulum L, in feet, and its period T, in seconds. To the nearest foot, which is the length of a pendulum with period 8 seconds?
The length of a pendulum with period 8 seconds would be, 316 feet.
What is Period of a simple pendulum?
The formula for the period T of a pendulum is T = 2π Square root of √L/g, where L is the length of the pendulum and g is the acceleration due to gravity.
The equation relating the period T and length L of a pendulum is given by:
T = 2π√(L/32)
We can rearrange this equation to solve for L in terms of T:
L = 32(T/2π)²
To find the length of a pendulum with period 8 seconds, we can substitute T = 8 into the above equation and solve for L:
L = 32(8/2π)²
L ≈ 316 feet
Rounding this value to the nearest foot, we get:
L ≈ 316 feet (to the nearest foot)
Therefore, The length of a pendulum with period 8 seconds would be, 316 feet.
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please help ,me for 30 points
Answer:
C
Step-by-step explanation:
To make it easy, if there are 3 yellow, 2 green, and 8 total, just find the equation that has the fraction result of 5/8.
What is the conversion of 31c to f ?
The value of conversion from Celsius to Fahrenheit for the value 31 Celsius is equal to 87.8 Fahrenheit.
Standard measuring units for the temperature is known as Celsius and Fahrenheit.
Formula used to convert the temperature from Celsius to Fahrenheit is written as
°F = 9 /5 ( ° C ) + 32.
Convert 31 Celsius to Fahrenheit by substituting the given value in the above formula :
= 9 /5 ( 31° ) + 32
= (1/5) (279° ) + 32
= 55.8° + 32
= 87.8°F
Therefore, the values after conversion for the 31Celsius to Fahrenheit is given by 87.8 Fahrenheit.
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The graph of y=f(x) is shown in the xy-plane
which equation defines function f?
the equation of the line will be 5y = 7x -7. Option c is correct.
What is the Linear equation?A linear equation is an algebraic equation of the form y = mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, a linear equation that passes through the points (5,0) and (0, -7)
The slope-intercept form of the equation of a line
y=mx+b,
where m is the slope
b is the y-intercept
since, slope = (y - y')/(x -x')
In our case,
slope = (-7 -0)/(0-5)
slope = 7/5
b = -7
thus,
the equation of the line will be:
y = 7/5x -7
multiply by 5 on both sides
5y = 7x -7
Therefore, the equation of the line will be 5y = 7x -7.
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what is derivative calculator with steps
A derivative calculator is an online application or programme that allows you to determine the derivative of a function fast and conveniently without having to complete the calculations by hand.
The derivative of a function tells you how the function is evolving at any given moment, and it is a key topic in calculus. Derivative calculators are important tools for students and professionals that need to rapidly and properly find derivatives.
To use a derivative calculator, enter the function to be differentiated and the calculator will calculate the derivative for you. To find the derivative, the calculator will employ differentiation methods such as the power rule, product rule, and chain rule.
For example, if you wanted to calculate the derivative of the function f(x) = [tex]x^{2}[/tex]+ 2x + 1, you would enter it into the derivative calculator, which would provide the result f'(x) = 2x + 2.
Depending on the amount of detail offered by the calculator, derivative calculators can also provide other information about the function, such as critical points, inflection points, and concavity.
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What is the conversion of 20 km in miles ?
The conversion of 20 km in miles is 12.42742 miles.
Kilometer (km) and mile are both units of distance or length, but they are used in different parts of the world.
A kilometer is a metric unit of length used in most countries outside the United States. It is defined as 1,000 meters, or approximately 0.62 miles.
To convert kilometers (km) to miles, you can use the conversion factor of 1 km = 0.621371 miles.
So, to convert 20 km to miles, you can multiply 20 by 0.621371:
20 km * 0.621371 miles/km = 12.42742 miles
Therefore, 20 kilometers is approximately equal to 12.42742 miles.
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if f(x) = ax² + bx + c for all x and if f( -3 ) = 0 and f( 1) = 0 then b + c =
a) -5
b) 1
c) -1
d) 5
if f f(x) = ax² + bx + c for all x and if f( -3 ) = 0 and f( 1) = 0 then b + c will be either 1,-5 or 5 depending on value of c.
What is a function?A relation is a function if it has only One y-value for each x-value.
Given that f(x) = ax² + bx + c for all x and
if f( -3 ) = 0 and
f( 1) = 0
We need to find the value of b+c
f(-3)=a(-3)² + b(-3) + c
f(-3)=9a-3b+c=0
9a-3b+c=0
We need to find the value of b + c, which is equal to -a.
From equation (2), we have:
a = -b - c
Substituting this value of a in equation (1), we get:
9(-b - c) - 3b + c = 0
-12b - 8c = 0
3b + 2c = 0
b = -(2/3)c
Substituting this value of b in equation (2), we get:
a + (-(2/3)c) + c = 0
a = (1/3)c
Therefore, b + c = -(2/3)c + c = (1/3)c
Hence, if f f(x) = ax² + bx + c for all x and if f( -3 ) = 0 and f( 1) = 0 then b + c will be either 1,-5 or 5 depending on value of c.
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Two vertices of a right triangle have coordinates (5, 12) and (11, 12). The segment that connects these points is a leg of the triangle.
Which coordinate pair for the third vertex would create a right triangle?
Responses
(19, 12)
, left parenthesis 19 comma 12 right parenthesis,
(8, 20)
, left parenthesis 8 comma 20 right parenthesis,
(8, 12)
, left parenthesis 8 comma 12 right parenthesis,
(11, 4)
, left parenthesis 11 comma 4 right parenthesis,
The answer is (A) (11, 4).
Step-by-step explanation: Given that two vertices of a right-angled triangle are A(5, 12) and B(11, 12).
We can plot the given points on the co-ordinate plane as shown in the attached figure.
We will then see that only the point C(11, 4) will lie exactly below the point B(11, 12). Also, the segment AB and BC are the legs of the triangle, AC is the hypotenuse.
The lengths of the three sides are
[tex]AB = 11 - 5 = 6\\\\BC = 12 - 4 = 8\\\\AC = \sqrt{AB^{2} +BC^{2} } = \sqrt{6x^{2}+8^{2} } = \sqrt{100} = 10[/tex]
Thus, the correct option is (A).
how many fps to mph?
We can convert fps to mph by using the relation, one mph = 1.18 fps.
One fps means one foot per second and one mph means one mile per hour. Foot and mile are the units of distance and second and hour are the units or time.
We have to convert fps to mph.
As per the standard unit conversion rates, we know,
One mile = 5280 foot.
Also, one hour = 3600 seconds.
So, if we want to convert, we should write,
= mph
= 4280/3600
= 1.18 fps.
So, now we have a standard relation that says, one mph is equal to 1.18 fps.
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the probability that a continuous random variable equals any of its values is_____
The probability that a continuous random variable will be equal to any specific value is zero. This is because the probability of an individual value for a continuous random variable is represented by the area under the probability density function (PDF) at that particular value, and the area of a single point is zero.
Randomization in an experiment is important because it ensures that:________
Randomization in an experiment is important because it ensures that the results achieved are accurate .
Randomization in an experiment refers to a random assignment of participants to the treatment in an experiment .
Randomizing the experiments can help you get the best cause-effect relationships among the variables. It helps in controlling the lurking variables . These variables can affect the results to be different from what they are supposed to be . Randomization prevents biases and makes the results fair.
For ensuring that the information obtained from the experiment is correct, A randomized experiment is perfect to help us .
Researchers control values of the explanatory variable with a randomization procedure. So, if we see a relationship between the explanatory variable and response variables, we can say that it is a causal one.
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A solid plastic ball is a sphere with radius in. How much plastic does it take to make one ball? Use 3.14 for .
This indicates that one solid plastic ball with a radius of one inch requires 4.19 cubic inches of plastic.
What is volume?The volume of an object or a substance can be calculated using various formulas, depending on the shape and dimensions of the object or substance. For instance, the volume of a cube can be calculated by multiplying the length, width, and height of the cube. Similarly, the volume of a cylinder can be calculated by multiplying the area of the circular base by the height of the cylinder. Volume is an important concept in many fields, including physics, chemistry, engineering, and architecture. In physics, the volume of a material is important in understanding its density and mass. In chemistry, the volume of a gas is related to its pressure and temperature through the ideal gas law. In engineering and architecture, volume is important in designing and constructing buildings, bridges, and other structures.
Here,
The formula for the volume of a sphere is given by:
V = (4/3) * π * r³
where V is the volume of the sphere and r is the radius.
Substituting the given radius of 1 inch and the value of π as 3.14, we get:
V = (4/3) * 3.14 * 1³ = 4.19 cubic inches
This means that it takes 4.19 cubic inches of plastic to make one solid plastic ball with a radius of 1 inch.
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